Discounting the Future

The culture of the 1970s in the United States of America was progressive and revolutionary. Due to various events that were unfavorable to the public, U.S. citizens began to lose trust in their government. Signs of the public's revolt and dissention began to show in laws and propositions voters passed. In California, Proposition 13 was one of many anti-tax laws taxpayers voted for to cut back the control of the government. As a result, revenues for public services and improvements decreased and maintenance allocations for infrastructure systems were considerably reduced. Fast-forwarding to today, infrastructure systems in the U.S. are reaching their retirement period and are requiring extreme maintenance and attention. Los Angeles has been experiencing severe water main breaks in its water distribution system for several years now, but the city is lacking funds to replace the aging pipes. The lack of funds paired with aging infrastructure indicates there is a flaw in the forecasting analysis techniques used today to project infrastructure costs. Therefore, an alternative discounting function to the exponential is proposed: the hyperbolic discounting function. A comparative analysis was performed using a hyperbolic and an exponential discounting function. The two functions were calibrated over the course of 50 years and the parameters r and a were determined. Then the discounts were applied to a 50-year expenditure projection for pipe replacements of a water distribution system. The present value was computed with each discount function and results were obtained. By year 50, the hyperbolic function yielded a higher present value of $25.06 million and the exponential function yielded a present value of $14 million. These results lead to the conclusion that the hyperbolic discounting function is the preferred methodology when calculating long-term expenditures, especially those dependent on tax revenue.